In the figure a worker lifts a weight by pulling down on a rope with a force . The upper pulley is attached to the ceiling by a chain,and the lower pulley is attached to the weight by another chain.The weight is lifted at constant speed. Assume that the rope,pulleys, and chains all have negligible weights.
A) In terms of ,find the tension in the lower chain.
B) In terms of ,find the tension in upper chain.
C) In terms of ,find the magnitude of the force if the weight is lifted at constant speed.
Until he was in his seventies, Henri LaMothe excited audiences by belly-flopping from a height of 13 m into 35 cm. of water. Assuming that he stops just as he reaches the bottom of the water and estimating his mass to be 72 kg, find the magnitudes of the impulse on him from the water.
In the figure below, the rolling axle, 1.43 m long, is pushed along horizontal rails at a constant speed .
A resistor ohm is connected to the rails at points a and b, directly opposite each other. (The wheels make good electrical contact with the rails, and so the axle, rails, and R form a closed-loop circuit. The only significant resistance in the circuit is R.) There is a uniform magnetic field vertically downward. Calculate the induced current I in the resistor and what horizontal force F is required to keep the axle rolling at constant speed?
A stream of water strikes a stationary turbine bladehorizontally, as the drawing illustrates. The incident water streamhas a velocity of +18.0 m/s, while the exiting water stream has avelocity of -18.0 m/s. The mass of water per second that strikesthe blade is 17.0 kg/s. Find themagnitude of the average force exerted on the water by theblade.
A 10.0 g marble slides to the left with a velocity ofmagnitude 0.300 m/s on thefrictionless, horizontal surface of an icy, New York sidewalk andhas a head-on elastic collision with a larger 25.0 g marble sliding to the right with a velocityof magnitude 0.150 m/s (Fig. 8.35).
(a) Find the velocity of each marble (magnitude anddirection) after the collision. (Since the collision is head-on,all the motion is along a line. Take right as the positivex direction.)
m/s (smaller marble)
m/s (larger marble)
(b) Calculate the change in momentum (that is, the momentum afterthe collision minus the momentum before the collision) for eachmarble.
kgm/s (smallermarble)
kgm/s (largermarble)
(c) Calculate the change in kinetic energy (that is, the kineticenergy after the collision minus the kinetic energy before thecollision) for each marble.
J (smaller marble)
J (larger marble)
Two snowcats tow a housing unit to a new location at McMurdo Base, Antarctica, as shown in the figure. The sum of the forces and exerted on the unit by the horizontal cables is parallel to the line L, and N. Determine ? Determine the magnitude of ?
(a) How far from a 50.0-mm-focal-length lens must an object be placed if its image is to be magnified 2.00 X and be real?
(b) What if the image is to be virtual and magnified 2.00 X?
Resolve the force F2 into components acting along the u and v axes and determine the magnitudes of the components.
A frictionless plane is 10.0 m long and inclined atA sled starts at the bottom with an initial speed of 5.00 m/s up the incline. When it reaches the point at which it momentarily stops, a second sled is released from the top of this incline with an initial speed v1 both sleds reach the bottom of thein cline at the same moment.
(a) Determine the distance that the first sled traveled up the incline.
(b) Determine the initial speed of the second sled.
A window washer of mass M is sitting on a platform suspended by a system of cables and pulleys. He is pulling on the cable with a force of magnitude F.The cables and pulleys are ideal (massless and frictionless), and the platform has negligible mass.
Find the magnitude of the minimum force F that allows the window washer to move upward.
Express your answer in terms of the mass M and the magnitude of the acceleration due to gravity g.
A potters wheel having a radius of 0.50 m and a moment of inertia of is rotating freely at 50 rev/min. The potter can stop the wheel in 6.0s by pressing a wet rag against the rim and exerting a radially inward force of 70N. Find the effective coefficient of kinetic friction between the wheel and the wet rag.
Starting with an initial speed of 5.00 m/s at a height of 0.300 m, a 1.50 kg ball swings downward and strikes a 4.60kg ballthat is at rest, as the drawing shows. a. using the principle of conservation of mechanicalenergy,find the speed of the 1.50 kg ball just before impact b. assuming that the collision is elastic, find the velocities( magnitude and direction ) of both balls just after thecollision c. how high does each abll swing after the collision, ignoringair resistance?
Two adults and a child want to push a wheeled cart in thedirection marked x in Fig. 4.29 The two adults push with horizontalforces as shown in the figure. (a)Find the magnitude and direction of the smallest force that thechild should exerts the minimum force found in part (a), the cartaccelerates at 2.0 in the +x direction. What is theweight of the cart?
An airplane pilot sets a compass course due west and maintainsan airspeed of 220 km/h. After flying for 0.500 h, she find sherself over a town 120 km west and 20 km south of her starting point. a) Find the wind velocity (magnitude and direction). b) If the wind velocity of 40 km/h due south, in what direction should the pilot set her course to travel due west? Use the same airspeed of 220 km/h.
The answers are:
a) 44.7 km/h, 26.6 deg. west of south
b) 10.5 deg. north of west
A spherical cavity is hollowed out of the interior of a neutral conducting sphere. At the center of the cavity is a point charge,of positive charge q.
A) What is the total surface charge q on the interior surface of the conductor (i.s., on the wall of the cavity)?
C) What is the magnitude of the electric field inside the cavity as a function of the distance from the point charge? Let k, as usual, denote .
D)Will the total charge on the surface of the cavity change?
Will the totaly charge on the exterior of the conductor change?
Will the charge on the electric field with in the cavity change?
Will the charge on the electric field outside the cavity change?
A constant potential difference of 12V is maintained between the terminals of a 0.25 micro-F parallel plate air capacitor.
A. A sheet of Mylar is inserted between the plates of the capacitor completely filling the space between the plates. When this is done how much additional charge flows into the positive plate of the capacitor? (K for mylar = 3.1)
B. What is the total induced charge on either face of the mylar sheet?
C. What effect does the mylar sheet have on the electric field between the plates? Explain how you can reconcile thiswith the increase of charge on the plates, which acts to increase the electric field.
In a truck-loading station at a post office, a small 0.200-kg package is released from rest a point A on a track that is one quarter of a circle with radius 1.60 m.The size of the packageis much less than 1.60m, so the package can be treated at aparticle. It slides down the track and reaches point B with a speed of 4.80 m/s. From point B, it slides on a level surface a distanceof 3.00 m to point C, where is comes to rest.
(a) What is the coefficient of kinetic friction on the horizontal surface?
(b) How much work is done on the package by friction as it slides down the circular arc from A to B?
A radar station, located at the origin of xz plane, as shown in the figure , detects an airplane coming straight at the station from the east. At first observation (point A), the position of the airplane relative to the origin is . The position vector has a magnitude of and is located at exactly above the horizon. The airplane is tracked for another } in the vertical east-west plane for , until it has passed directly over the station and reached point B. The position of point B relative to the origin is (the magnitude of is ). The contact points are shown in the diagram, where the x axis represents the ground and the positive z direction is upward.
Define the displacement of the airplane while the radar was tracking it: . What are the components of
Express in meters as an ordered pair, separating the x and z components with a comma, to two significant figures.
The magnetic field in acertain region is 0.128 ,and its direction is that of the z-axis in the figure.
Part A
What is the magnetic flux across the surface abcd in the figure?
Part B
What is the magnetic flux across the surface befc ?
Part C What is the magnetic flux across the surface aefd?
Part D
What is the net flux through all five surfaces that enclose the shaded volume?
A marble moves along the x-axis. The potential-energy functionis shown in Fig. 1
a) At which of the labeled x-coordinates is the force on the marble zero?
b) Which of the labeled x-coordinates is a position of stable equilibrium?
c) Which of the labeled x-coordinates is a position of unstable equilibrium?